GPELab, a Matlab toolbox to solve Gross–Pitaevskii equations I: Computation of stationary solutions. This paper presents GPELab (Gross–Pitaevskii Equation Laboratory), an advanced easy-to-use and flexible Matlab toolbox for numerically simulating many complex physics situations related to Bose–Einstein condensation. The model equation that GPELab solves is the Gross–Pitaevskii equation. The aim of this first part is to present the physical problems and the robust and accurate numerical schemes that are implemented for computing stationary solutions, to show a few computational examples and to explain how the basic GPELab functions work. Problems that can be solved include: 1d, 2d and 3d situations, general potentials, large classes of local and nonlocal nonlinearities, multi-components problems, and fast rotating gases. The toolbox is developed in such a way that other physics applications that require the numerical solution of general Schrödinger-type equations can be considered.

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  1. Antoine, Xavier; Zhao, Xiaofei: Pseudospectral methods with PML for nonlinear Klein-Gordon equations in classical and non-relativistic regimes (2022)
  2. Huang, Pengfei; Yang, Qingzhi: Newton-based methods for finding the positive ground state of Gross-Pitaevskii equations (2022)
  3. Jiang, Chaolong; Cui, Jin; Qian, Xu; Song, Songhe: High-order linearly implicit structure-preserving exponential integrators for the nonlinear Schrödinger equation (2022)
  4. Bernier, Joackim; Crouseilles, Nicolas; Li, Yingzhe: Exact splitting methods for kinetic and Schrödinger equations (2021)
  5. Forbes, Dominique; Rebholz, Leo G.; Xue, Fei: Anderson acceleration of nonlinear solvers for the stationary Gross-Pitaevskii equation (2021)
  6. Heid, Pascal; Stamm, Benjamin; Wihler, Thomas P.: Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation (2021)
  7. Wang, Lan; Cai, Wenjun; Wang, Yushun: An energy-preserving scheme for the coupled Gross-Pitaevskii equations (2021)
  8. Antoine, Xavier; Geuzaine, Christophe; Tang, Qinglin: Perfectly matched layer for computing the dynamics of nonlinear Schrödinger equations by pseudospectral methods. Application to rotating Bose-Einstein condensates (2020)
  9. Cui, Jin; Cai, Wenjun; Jiang, Chaolong; Wang, Yushun: A new linear and conservative finite difference scheme for the Gross-Pitaevskii equation with angular momentum rotation (2019)
  10. Kochetov, Bogdan A.: Mutual transitions between stationary and moving dissipative solitons (2019)
  11. Antoine, Xavier; Hou, Fengji; Lorin, Emmanuel: Asymptotic estimates of the convergence of classical Schwarz waveform relaxation domain decomposition methods for two-dimensional stationary quantum waves (2018)
  12. Antoine, Xavier; Tang, Qinglin; Zhang, Yong: A preconditioned conjugated gradient method for computing ground states of rotating dipolar Bose-Einstein condensates via kernel truncation method for dipole-dipole interaction evaluation (2018)
  13. Antoine, X.; Lorin, E.: Multilevel preconditioning technique for Schwarz waveform relaxation domain decomposition method for real- and imaginary-time nonlinear Schrödinger equation (2018)
  14. Karasözen, Bülent; Uzunca, Murat: Energy preserving model order reduction of the nonlinear Schrödinger equation (2018)
  15. Ruan, Xinran: A normalized gradient flow method with attractive-repulsive splitting for computing ground states of Bose-Einstein condensates with higher-order interaction (2018)
  16. Antoine, Xavier; Levitt, Antoine; Tang, Qinglin: Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods (2017)
  17. Antoine, X.; Lorin, E.: An analysis of Schwarz waveform relaxation domain decomposition methods for the imaginary-time linear Schrödinger and Gross-Pitaevskii equations (2017)
  18. Henning, Patrick; Peterseim, Daniel: Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials (2017)
  19. Wu, Xinming; Wen, Zaiwen; Bao, Weizhu: A regularized Newton method for computing ground states of Bose-Einstein condensates (2017)
  20. Antoine, Xavier; Besse, Christophe; Rispoli, Vittorio: High-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrödinger/Gross-Pitaevskii equations (2016)

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